Geodesic
A New Convexity Property for Monotone Operators
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 883-887

Voir la notice de l'article provenant de la source Heldermann Verlag

It is well known that the interior of the domain of a maximal monotone operator is convex, and coincides with the core of its convex hull. In fact this is also true for the interior of the difference of the domains of two maximal monotone operators S and T. Recently, J. Borwein ["Maximal monotonicity via convex analysis, J. of Convex Analysis 13 (2006), this issue] used the condition that the origin is in the core of the convex hull of the difference of the graphs of S and -T in order to obtain that the origin is in the image of S+T. In this short note we show that gph(S) - gph(-T) has similar properties to dom(S) - dom(T). 
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     author = {C. Zalinescu},
     title = {A {New} {Convexity} {Property} for {Monotone} {Operators}},
     journal = {Journal of convex analysis},
     pages = {883--887},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a25/}
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C. Zalinescu. A New Convexity Property for Monotone Operators. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 883-887. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a25/